Prove that 1C1−2C2+3C3−4C4++n(−1)n−1Cn=1+21+31++n1˙

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Prove that {{{C}_{{1}}}}{{1}}-{{{C}_{{2}}}}{{2}}+{{{C}_{{3}}}}

Question

Prove that $\frac{C _{1}}{1} - \frac{C _{2}}{2} + \frac{C _{3}}{3} - \frac{C _{4}}{4} + + \frac{( - 1 ) ^{n - 1}}{n} C_{n} = 1 + \frac{1}{2} + \frac{1}{3} + + \frac{1}{n} ˙$

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Prove that

\frac{C _{1}}{1} - \frac{C _{2}}{2} + \frac{C _{3}}{3} - \frac{C _{4}}{4} + + \frac{( - 1 ) ^{n - 1}}{n} C_{n} = 1 + \frac{1}{2} + \frac{1}{3} + + \frac{1}{n} ˙

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Question Text

Prove that

\frac{C _{1}}{1} - \frac{C _{2}}{2} + \frac{C _{3}}{3} - \frac{C _{4}}{4} + + \frac{( - 1 ) ^{n - 1}}{n} C_{n} = 1 + \frac{1}{2} + \frac{1}{3} + + \frac{1}{n} ˙